Question: How do you determine how old soil is? Knowing the different interactions it has with time, climate, and living organisms.

This is a fantastic question!
You obviously know something about ClORPT, the five factors of soil formation. For others who read this answer, and may not be, a summary of the ClORPT factors occurs below the answer.
It is easier to determine relative ages than actual ages, so here are a few guiding factors we use. We identify the relative age of a soil by the amount of development we see in terms of how distinct the horizons (layers with similar color, texture, structure and chemical properties) are, and the types of minerals that are present (as minerals age, particularly clay minerals, they go through distinct stages that can be equated with the amount of weathering they have experienced, and thus a relative age).
Relief/topography: how old and stable is the landscape on which the soil is forming. Relatively flat upland positions are more stable than slopes and bottoms. So soils on the uplands tend to have more development because on slopes tends to remove the surface soil which limits the amount of soil formation that can occur. Likewise, the soil eroded from the slopes is deposited in the bottoms, and soil formation is continually rebooting every time new materials are deposited on top. This is the reason soils at the base of slopes, and especially on flood plains are typically young.
Organisms contribute especially to the development of the A horizon (surface horizon or topsoil) as they contribute organic matter. Beyond that, organisms do not have a great effect on the age of a soil.
In general, soils in hot and humid environments (like the southeastern USA or tropical rainforests tend to be more developed than soils in cooler or drier environments. They may not be older in terms of actual time or years, but in terms of weathering of the minerals present and amount of horizon development, they are definitely older. Exceptions to this rule occur in some deserts which are on stable landscapes, and the soils have a lot of horizon development, but it occurred in times of previous climates such as ice ages when the climate was wetter. Little development happens in deserts because there is almost no water moving through the soil and almost no vegetation growing. In many deserts much of the topsoil has been removed due to wind or water erosion leaving a stone pavement.
And you missed an important one that sometimes is related to landscapes and topography, but what kinds of parent materials are present, in other words, what is the stuff in which the soil is forming. If the soil is forming in bedrock, the rate of soil formation is affected by the rate of weathering of the bedrock: sandstones often weather more easily than limestones or shales. Soils forming on glacial depositions cannot be any older than the time the glacier receded. And one of my favorites to observe is in western New Mexico and Arizona, USA, where volcanic activity has left lava flows of different ages. You can look at the kind and amount of vegetation growing, and the amount and depth of weathering of the lava to determine the relative age of the flows as well as the relative ages of the soils forming in them.

Cl – Climate. This is primarily how hot/cold/seasonal the temperature is, and how much precipitation comes in what form and when. These factors affect the rate of weathering of minerals, which plants grow, and how much water moves through a profile.
O – Organisms. Primarily these organisms are plants, as soils that form under trees are much different than soils that form under grasses. But it also includes other organisms such as earthworms, ants, bacteria, and fungi, among many others, that alter the soil through decomposition of organic materials and mixing.
R – Relief, topography. This is the shape of the landscape, hills, slopes, valleys, mountains, plateaus, and plains. Deeper soils form on stable landscapes such as plains or plateaus. Soils erode from hillsides and are deposited in valleys; both these processes limit soil formation.
P – Parent material. This is the rock, minerals, and sediments in which the soil forms. The type of rock and minerals affects the rate of weathering, the chemical composition of the soil, and the grain size of the particles. Sediments have been moved and deposited by wind, water, gravity, or ice. The nature of these sediments affect many soil physical and chemical properties.
T – Time. Nothing happens apart from the passage of time. The longer a landscape is stable, the longer ClORP have to work, which increases the potential for soil formation.